Is 1-2sin^2(x)=2cos^2(x)-1 ?

The answer to whether 1-2sin^2(x)=2cos^2(x)-1 is True

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prove 1-2sin^2(x)=2cos^2(x)-1

prove

1 - 2 sin^{2} (x) = 2 cos^{2} (x) - 1

True

Solution steps

1 - 2 sin^{2} (x) = 2 cos^{2} (x) - 1

Manipulating left side

1 - 2 sin^{2} (x)

Rewrite using trig identities

= 2 cos^{2} (x) - 1

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (θ) - tan^{2} (θ) = 1

\frac{1 + tan ^{2} ( x )}{tan ^{2} ( x )} = csc^{2} (x)

\frac{1}{sec ^{2} ( x )} + \frac{1}{csc ^{2} ( x )} = 1

(1 + tan^{2} (x)) cot^{2} (x) = csc^{2} (x)

csc (θ) sec (θ) - cot (θ) = tan (θ)

Is 1-2sin^2(x)=2cos^2(x)-1 ?
The answer to whether 1-2sin^2(x)=2cos^2(x)-1 is True